10ème Congrès Français d'Acoustique
Lyon, 12-16 Avril 2010
Experimental Study on Thermoacoustic Cooling System with Two Stacks in
a Straight Resonator Tube
Ikhsan Setiawan1,2, Agung Bambang Setio-Utomo1, Makoto Nohtomi2, and Masafumi Katsuta2
2
1
Physics Department, Gadjah Mada University, Indonesia
Graduate School of Environment and Energy Engineering, Waseda University, Japan
It has been done an experimental study of the use of two stacks 1 and 2 in a straight resonance tube of a
thermoacoustic cooling system. We used a half-wavelength straight resonance tube at which the one end is
closed by a rigid plug and the other end is closed by a plastic diaphragm which can vibrate axially due to sound
wave produced by a loudspeaker facing to it. The tube is PVC pipe and filled by free air at atmospheric pressure
and has 112 cm of length so it gives a calculated operating frequency around 152 Hz. The stacks are parallel
plates type, which have plates thickness of 0.3 mm, and the plates spacing of 0.85 mm which is around four
times of the thermal penetration depth. The diameter of stack is the same as the inner diameter of the tube, i.e.
4.6 cm, while the length of stack is 10 cm. We varied the sound frequency in the range of 130 – 160 Hz, the
input electric power of loudspeaker from 40 W until 160 W, and the location of the center of the each stack in
the range of 8 – 25 cm measured from each end of the tube, to investigate the their influences to the temperature
decrease which can be achieved. It is found that the temperature decreases of the two cooling points 1 and 2
reached maximum at sound frequency of 147 Hz and when the two stacks were placed near to the ends of the
tube. It is also found that a higher electric power tends to produce a larger temperature decrease. At 90 W of the
input electric power, the maximum temperature decrease around 9.8 °C was obtained at cooling point 1 when the
center of the stack 1 was placed at 80 mm from the rigid closed end of the tube.
1
Introduction
Thermoacoustic refrigerator is an alternative cooling
system which is environmentally friendly due to the use of
non-chlorofluorocarbon or non-hydro-fluorocarbon gas as
working medium, i.e. it uses air or noble gas. This system
uses a high intensity sound wave to provide work for
transferring heat from the cold to the hot regions through a
stack in resonator tube of the system. The description on
the basic principles of work of this apparatus has been
discussed by Wheatley [1]. Wetzel and Herman [2] have
described the guideline for design optimization of
thermoacoustic refrigerator. Zoontjens et al [3] have
constructed a low-cost loudspeaker-driven thermoacoustic
refrigerator.
Thermoacoustic refrigerator basically consists of an
acoustic driver (loudspeaker) coupled with a resonator tube
which is filled with a working gas. A standing sound wave
with a high intensity can be established in the resonator
tube by the loudspeaker. In the tube, a stack is installed near
pressure antinode of the sound wave. This stack separates
the cooling region in where the gas parcel expands, and the
heating region in where the gas parcel compresses. The
cooling and heating processes occur due to the heat
exchange between the gas and the stack layers. The net
effect is the heat flow takes place from the cool to the hot
sides, i.e. in the direction to the pressure antinode.
Typically, the simplest resonator for thermoacoustic
refrigerator is a straight tube with one end closed and the
other is open to which the acoustic driver is coupled,
forming a quarter-wavelength resonator tube. In this case,
we have only one pressure antinode, and we put the one
stack near it. Otherwise, if we use a half-wavelength
resonator tube which both ends are closed, we will possess
two pressure antinodes
Fig.1 The schematic diagram of the thermoacoustic
cooling system with two stacks in a half-wavelength
resonator tube.
at the both closed end. If we then put two stacks near the
pressure antinodes, we will have two cooling points and
two heating point, the heat flows occur in opposite direction
regarded to the stacks which basically give one cooling
region in the middle of the resonator tube (Fig. 1). In this
paper, we describe an experimental study of a
thermoacoustic cooling sys-tem with two stacks in a
straight resonator tube.
2
Theory
The total rate of heat flux Q& pumped acoustically
along the stack is approximately (by neglecting viscous
losses) given by [4]
1
Q& = − Π δ κ Tm βp1u1 (Γ − 1)
4
(1)
where Π is the perimeter of the stack plate in the
direction normal to the axis of the resonator, δ κ is the
thermal penetration depth of the gas, Tm is the mean of
absolute temperature of the gas, β is the coefficient of
mm in diameter which are glued to the plates. The stacks
have length of 10 cm, diameter is the same as inner
diameter of the resonator tube, i.e. 4.6 cm, and the cross
sections are shown in Fig 2. In our condition for air at
room temperature of 30 °C, the thermal penetration depth at
frequency 152 Hz is around 0.215 mm, and our plate
spacing is around 4δ κ .
25
∇Tcrit
T βωp1
= m
ρ m c p u1
Pressure amplitude (a.u.)
thermal expansion of the gas, p1 is the pressure amplitude,
u1 is particle velocity amplitude, and Γ is the ratio of the
temperature gradient across the stack ( ∇Tm ) to a critical
mean-temperature gradient ( ∇Tcrit ). The critical meantemperature gradient which is given by [4]
(2)
0
where κ is thermal conductivity, ρ is density, c p is isobaric specific heat of the gas, and f is sound frequency.
3
Experimental Method
Our thermoacoustic cooling system is schematically
depicted in Fig 1. We used a PVC pipe of 112 cm long and
4.6 cm of inner diameter, one end is closed by a copper
rigid plug and the other end is closed by a thin plastic
diaphragm. The “diaphragm end” is assembled on a
loudspeaker box in where a 10 inches loudspeaker of 200
W 4 Ω is installed. The sound produced by the loud
speaker will make the diaphragm vibrates axially and so
create a half-wavelength of standing sound wave inside the
resonator tube. The resonator was filled with free air at
atmospheric pressure and has a calculated resonance
frequency around 152 Hz (for a half-wavelength tube). The
resonance frequency is usually used as the operating
frequency.
Figure 2. The cross section of the parallel plate stacks.
The stack’s housings are 2 in. PVC pipe.
We made two stacks of parallel plate type. The plate
material is plastic which roughly has thermal conductivity
in the range of 0.1 – 0.6 W/m K and specific heat around
1.3 kJ/kg K [6]. The plate thickness is 0.3 mm. To provide
space between plates, we used nylon fishing lines of 0.85
20
40
60
80
100
Distance from rigid end (cm)
Figure 3. The relative pressure amplitude distribution in
the resonator tube.
per unit mass of the gas. While the thermal penetration
depth is given by [5]
(3)
15
10
where ω is the angular frequency of the acoustic wave,
ρ m is the mean density and c p is the isobaric heat capacity
κ
δκ =
πfρc p
20
To ensure the presence of a half-wavelength of sound
standing wave inside the resonator tube, we measured the
relative amplitudes of pressure in the tube along the axis by
using a small microphone and observed the FFT signal on a
computer.
The temperature measurements were done by using
four digital thermometers with LM35 temperature sensors,
and carried out for various frequencies, input electric
powers, and locations of the two stacks in the resonator
tube.
4
Results and Discussion
The measurement results of the relative pressure
amplitude distribution in the resonator tube at a driving
frequency of 152 Hz is shown in Fig. 3. This confirmed that
a half-wavelength of sound standing wave was present in
the resonator tube. It can be seen that the pressure node was
not exactly at the middle of the length of the tube and
somewhat shifted toward to the diaphragm end due to the
use of this diaphragm.
Based on this result, then we put stack 1 and stack 2
inside the tube each near the pressure antinodes, and it is
expected that the heat will flow through the stacks to the
middle of the the tube.
Fig. 4 depicts the typical result of the temperature
measurements at the cooling and the heating points. In this
case, the temperature decrease at the cooling point 1 (near
rigid end) is greater than that of the cooling point 2 (near
diaphragm), and conversely the temperature increase at the
heating point 1 was smaller than that of the heating point 2,
so that the temperature difference after 15 minutes, between
heating and cooling points for each stack, are not so
different.
The measurements of the temperature decrease at the
cooling points for various sound frequencies give a result as
shown in Fig 5. It shows that, in this case, the temperature
decrease at the cooling point 1 is always greater than that of
at the cooling point 2. In addition, it can be inferred from
the figure that the operating sound frequencies are roughly
in the range of 140 - 150 Hz which gives maximum temperature decrease. This operating frequency range is slightly
below the calculated resonance frequency of 152 Hz for a
half-wavelength resonator tube of 112 cm length. The
presence of the stack in the tube and the use of diaphragm
at one end of the tube were suspected to be the causes of the
shift in operating frequency from the expected value.
Temperature decrease (oC)
40
35
Temperature (oC)
(a)
10
8
Stack 2 fixed at 102 cm
from the rigid end.
6
4
2
Cooling point 1
Cooling point 2
0
30
0
25
(b)
10
Heating point 1
Heating point 2
15
0
5
Temperature decrease (oC)
20
Cooling point 1
Cooling point 2
10
Time (minutes)
15
Figure 4. Temperature changes in time of the cooling
and heating points 1 and 2 at frequency of 147 Hz and input
power of 90 W.
10
20
30
Distance of the center of stack 1 from the rigid end of
the tube (cm).
8
Stack 1 fixed at 10 cm
from the rigid end.
6
4
2
Cooling point 1
10
Cooling point 2
0
80
Temperature decrease (oC)
8
110
Figure 7. The temperature decrease: (a) for various
location of stack 1 (stack 2 fixed at 102 cm from rigid end),
and (b) for various location of stack 2 (stack 1 fixed at 10
cm from rigid end).
6
4
2
Cooling point 1
Cooling point 2
0
125
135
145
155
Sound frequency (Hz)
165
Figure 5. The temperature decreases for various sound
frequencies.
The dependency of temperature decrease on the input
electric power of loudspeaker can be seen on the Fig 6. It
points out the tendency that the temperature decrease will
be greater when we used the higher power input. Because
this cooling system did not use any heat exchangers, the
higher power input gave a greater heating in the hot side,
and did not significantly enhance the temperature decrease
due to the heat conduction through the stack.
10
Temperature decrease (oC)
90
100
Distance of the center of stack 2 from the rigid end of
the tube (cm)
8
6
4
2
Cooling point 1
Cooling point 2
Fig. 7 shows the influence of stacks location in the
tube on the temperature decrease at the cooling points 1 and
2. In Fig. 7(a), the location of the center of stack 1 was
varied from 8 cm until 25 cm measured from the rigid end
of the tube, while the center of stack 2 was fixed at 102 cm.
Whereas in Fig. 7(b), the center of stack 1 was fixed at 10
cm, and the center of stack 2 was varied from 86 until 104
cm measured from the rigid end of the tube. It is clearly
seen that the temperature decrease are greater when the
stacks are each nearer to the ends of the tube, i.e. nearer to
pressure antinodes. According to Eq.(2), the rate of the heat
transfer is proportional to the product
. So when the
stack is nearer to the closed end of the tube then it means a
and a smaller ; and a smaller
gives a lesser
greater
viscous loss. As a result, in this case, the cooling process is
greater when the stack is located nearer to the both closed
ends of the resonator tube.
The other fact which is shown by Fig. 7 is, again, the
temperature decrease of the cooling point 1 is always
greater then that of the cooling point 2. This shows that, in
this case, the use of our diaphragm did not give a good
cooling process in the stack near the diaphragm end. We
sure that if we could make a better diaphragm, or we
modify the loudspeaker so that its coupling with the tube
make a closed end (pressure antinode), then the cooling at
cooling point 2 would be better.
0
0
40
80
120
160
Input power (watt)
Figure 6. The temperature decrease for various input
electric power.
5
Conclusion
It has been built a thermoacoustic cooling system with
two stacks in a straight resonance tube. The tube is a half-
wavelength resonator with one end is closed by a rigid plug
and the other end is closed by a plastic diaphragm. It was
found a range of operating frequency of sound which give a
maximum temperature decrease. This operating frequency
was slightly below the calculated resonance frequency for a
half-wavelength tube. The magnitude of temperature
decrease was roughly proportional to the input electric
power of the loudspeaker. The temperature decrease of the
cooling point near the diaphragm is smaller than that of the
cooling point near the rigid end. It is suggested to make a
better diaphragm, or modify the loudspeaker so that it can
give a better cooling at cooling point near the diaphragm.
The investigation on the influence of stack location yield
that the temperature decrease of the cooling points 1 and 2
tend to be greater when each of the stacks are placed nearer
to each end of the tube.
Acknowledgement
This research was supported by Competitive Grant
Research Project XVI, Directorate General of Higher
Education, Department of National Education, Republic of
Indonesia.
Références
[1]
Wheatley, J., Hofler, T., Swift, G.W., Migliori, A.,
“Understanding some simple phenomena in
thermoacoustics with applications to acoustical heat
engines”, Am. J. Phys 53, 147−162 (1985).
[2]
Wetzel, M., Herman, C., “Design optimization of
thermoacoustics refrigerators”, Int. J. Refrig. 20,
3−21 (1997).
[3]
Zoontjens, L., Howard, C.Q., Zander, A.C.,
Cazzolato, B.S., “Development of a low-cost
loudspeaker-driven thermoacoustic refrigerator”,
Proc. Accoustics 2005 (2005).
[4]
Swift, G.W., “Thermoacoustic engines”, J. Acoust.
Soc. Am. 84, 1145-1180 (1988).
[5]
Tijani, M.E.H., Zeegers, J.C.H., de Waele, A.T.A.M,
“The optimal stack spacing for thermoacoustic
refrigeration”, J. Acoust. Soc. Am. 112(1), 128−123
(2002).
[6]
Plastic
reference
data,
inc.com/Plastic data.htm
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